Article
Mathematics, Interdisciplinary Applications
A. Moujahid, F. Vadillo
Summary: Mathematical modeling is crucial for studying the impact of delay in neural systems and evaluating its effects on the signaling activity of coupled neurons. This study focuses on the energy perspective of delayed coupling in Hindmarsh-Rose burst neurons, examining the average energy consumption required to maintain cooperative behavior and quantifying the contribution of synapses to total energy consumption.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Sajedeh Aghababaei, Sundarambal Balaraman, Karthikeyan Rajagopal, Fatemeh Parastesh, Shirin Panahi, Sajad Jafari
Summary: This paper investigates the influence of autaptic connections on chimera states, showing that the occurrence domain of chimeras is affected differently by coupling strength and autapse parameters. By adjusting the coupling strength and autapse parameters, an ideal dynamical state can be achieved.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics
Mahtab Mehrabbeik, Atefeh Ahmadi, Fatemeh Bakouie, Amir Homayoun Jafari, Sajad Jafari, Dibakar Ghosh
Summary: In network analysis, pairwise connections often overlook the higher-order connections among network nodes. However, these higher-order connections become more important in neuronal network synchronization, where simplicial complexes can represent non-pairwise connections. Map-based models offer a solution by reducing computational costs and increasing efficiency. This paper investigates the impact of pairwise and non-pairwise neuronal interactions on synchronization using memristive Hindmarsh-Rose neuron maps, showing that neurons can achieve synchrony with weak coupling strengths through chemical pairwise and non-pairwise synapses.
Article
Mathematics, Interdisciplinary Applications
Danila M. Semenov, Alexander L. Fradkov
Summary: This paper focuses on the adaptive synchronization problem in the heterogeneous Hindmarsh-Rose neuronal networks, studying the impact of heterogeneity on synchronization and proposing an adaptive algorithm for adjusting coupling strength to achieve network synchronization.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Yuncheng You
Summary: A new model of neural networks based on the memristive Hindmarsh-Rose equations is proposed. It is proven that exponential synchronization at a uniform convergence rate occurs when the coupling strengths satisfy the threshold conditions quantitatively expressed by the parameters, through sharp and uniform grouping estimates and by leverage of integral and interpolation inequalities tackling the linear network coupling against the memristive nonlinearity.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2023)
Article
Mathematics, Interdisciplinary Applications
Dan Liu, Song Zhao, Xiaoyuan Luo, Yi Yuan
Summary: The study focuses on the generalized projective synchronization problem of fractional-order extended Hindmarsh-Rose neuronal models with magneto-acoustical stimulation input. An NN sliding mode algorithm is derived to achieve synchronous control of neurons, allowing the master-slave neuron system to achieve GPS in a finite amount of time and exhibit resilience towards uncertain parameters and external disturbances.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Computer Science, Information Systems
Alexander L. Fradkov, Aleksandr Kovalchukov, Boris Andrievsky
Summary: In this paper, a new adaptive model for neurons based on the Hindmarsh-Rose third-order model is proposed. The learning algorithm for adaptive identification of neuron parameters is analyzed theoretically and through computer simulation. The algorithm is based on the Lyapunov functions approach and a reduced adaptive observer, allowing for parameter estimation of synchronized neuron populations. Rigorous stability conditions for synchronization and identification are presented.
Article
Engineering, Mechanical
Armand Sylvin Eteme, Conrad Bertand Tabi, Jean Felix Beyala Ateba, Henry Paul Ekobena Fouda, Alidou Mohamadou, Timoleon Crepin Kofane
Summary: The study demonstrates that the electromagnetic induction phenomenon can suppress chaotic states and enhance neural synchrony in neural systems. Increasing memristor strength can reduce the threshold for achieving synchronized states in electrically coupled neuron systems.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics
Branislav Rehak, Volodymyr Lynnyk
Summary: An algorithm for synchronization of interconnected Hindmarsh-Rose neurons network is presented, incorporating delays and noise in the network. The synchronization algorithm utilizes convex optimization and linear matrix inequalities formulation, showing synchronized recovery and adaptation variables through the minimum-phase property of the Hindmarsh-Rose neuron. The results are demonstrated with an example.
Article
Engineering, Mechanical
L. Messee Goulefack, A. Cheage Chamgoue, C. Anteneodo, R. Yamapi
Summary: In this study, we modified the Hindmarsh-Rose neuron model to account for the effect of electromagnetic induction on membrane potential. We found that increasing magnetic flux reduces the number of equilibrium points and enhances their stability. As a result, electromagnetic induction tends to regularize chaotic regimes and affect regular and quasi-regular states by reducing the number of spikes or even destroying oscillations.
NONLINEAR DYNAMICS
(2022)
Article
Physics, Multidisciplinary
Zeric Tabekoueng Njitacke, Sishu Shankar Muni, Soumyajit Seth, Jan Awrejcewicz, Jacques Kengne
Summary: This study focuses on the collective behavior of two HR neurons and a network of HR neurons. By connecting a traditional 3D HR neuron and a memristive 2D HR neuron through a gap junction, the collective behavior of the coupled neurons is obtained. Numerical simulations reveal that the coupled neurons exhibit various behaviors, including periodic, quasi-periodic, and chaotic bursting or spiking, by adjusting the control parameter. The network topology affects the spatiotemporal patterns, with cluster states observed in non-homogenous ring and star structures.
Article
Mathematics, Applied
Fatemeh Parastesh, Mahtab Mehrabbeik, Karthikeyan Rajagopal, Sajad Jafari, Matjaz Perc
Summary: This study investigates the higher-order interactions among neurons and finds that second-order interactions can lead to synchronization under lower first-order coupling strengths. Additionally, the introduction of three-body interactions reduces the overall synchronization cost.
Article
Mathematics, Applied
Yeyin Xu, Ying Wu
Summary: In this paper, analytical predictions of the firing cascades in a Hindmarsh-Rose neuron system are completed via an implicit mapping method. The obtained results provide new perspectives to the complex firing dynamics of the HR neuron system and present a potential strategy to regulate the firings of neurons.
Article
Computer Science, Artificial Intelligence
S. A. Malik, A. H. Mir
Summary: Efficient mathematical modeling and implementation are crucial for understanding the biological brain as an information processing system. The fractional order derivative is a great tool for modeling biological neurons due to its higher memory characteristics. This article presents a piecewise linear modification of fractional order Hindmarsh-Rose (HR) neuron, which mimics real neuron behaviors.
IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE
(2021)
Article
Mathematics, Applied
Xuerong Shi, Zuolei Wang
Summary: In this study, an extended Hindmarsh-Rose neuron model and the corresponding fractional-order neuron model with no equilibrium point are proposed. The hidden attractors of the neuron model are analyzed by changing system parameters and the order of the fractional-order neuron system. Hybrid projective synchronizations of the proposed neurons are investigated by designing suitable controllers according to fractional stability theory. The validity of the theoretical results is verified through numerical simulations. Overall, the research results have potential applications in understanding the dynamics of neuron systems and controlling their behaviors.
Article
Physics, Multidisciplinary
Tinggui Chen, Baizhan Xia, Dejie Yu, Chuanxing Bi
Summary: This study proposes a gradient phononic crystal structure for enhanced acoustic sensing. By breaking the symmetry of the PC structure, topologically protected edge states are introduced, resulting in topological acoustic rainbow trapping. The robustness and enhancement properties are verified numerically and experimentally.